Solve for $x$ and $y$ using elimination. ${-5x+3y = -34}$ ${-6x+3y = -42}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${-5x+3y = -34}$ $6x-3y = 42$ Add the top and bottom equations together. ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-5x+3y = -34}\thinspace$ to find $y$ ${-5}{(8)}{ + 3y = -34}$ $-40+3y = -34$ $-40{+40} + 3y = -34{+40}$ $3y = 6$ $\dfrac{3y}{{3}} = \dfrac{6}{{3}}$ ${y = 2}$ You can also plug ${x = 8}$ into $\thinspace {-6x+3y = -42}\thinspace$ and get the same answer for $y$ : ${-6}{(8)}{ + 3y = -42}$ ${y = 2}$